# Communication complexity and query complexity model

I have some doubts for the relationship between communication complexity model and query complexity model. In my understanding, query complexity model are same as decision tree complexity model. Let $$F(x, y) = f(g(x_{1}, y_{1}), ..., g(x_{n}, y_{n}))$$, then based on lifting theorems, if the dimension $$d$$ of binary strings is large enough, then deterministic communication complexity of $$F$$ is equal up to $$d$$ times the decision tree complexity of of $$f$$.

My question is, could we basically draw the claim that all the complexity result on computing certain $$f$$ we obtain on query complexity model is similar (with some constant factor) as in communication complexity model on computing certain $$F$$, at least when $$d$$ is large ?